After ran the pipeline, we are left with a handful of our best candidates to continue validating. The next filter they need to pass is a decent magnetocrystalline anisotropy energy.
Check out Will's writeup on the methodology:
Detailing our open experimentation with SakanaAI's Treequest algorithm, AB-MCTS, and its potential applicability in rare-earth free permanent magnet discovery.
Findings from the first pass at tree searching
For reference, the MAE model predicts FePt at 3.07 meV. This is really good! I haven't directly tested Nd₂Fe₁₄B but literature reports values around 2.9 meV per unit cell. Anything above ~2.5 is likely to be a good candidate! Most materials are less than 0.1 meV so when you have values of multiple meV that's a solid material.
Now let's take a look at some of the top candidates:
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -31.6444 eV; energy change = -0.0024 eV; symmetry: Pmm2 → Pmm2
Number of atoms in the cell: 4
Magnetization density: 0.118825
e_above_hull: 0.066408 eV/atom
Curie temperature: 672.8 K
No imaginary modes detected
Easy axis z: -9789.619323 eV (θ=0.0°, φ=0.0°)
Hard axis x: -9789.619306 eV (θ=90.0°, φ=0.0°)
ΔMAE (hard-easy): 0.016494 meV
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -27.9506 eV; energy change = 0.0000 eV; symmetry: Pmmm → Pmmm
Number of atoms in the cell: 4
Magnetization density: 0.096695
e_above_hull: 0.0 eV/atom
Curie temperature: 591.84 K
No imaginary modes detected
Easy axis z: -9206.405781 eV (θ=0.0°, φ=0.0°)
Hard axis x: -9206.402854 eV (θ=90.0°, φ=0.0°)
ΔMAE (hard-easy): 2.927303 meV
Great first result. Checks all our boxes. Slightly low on the magnetic saturation.
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -28.3771 eV; energy change = -0.0092 eV; symmetry: Pmm2 → Pmm2
Number of atoms in the cell: 4
Magnetization density: 0.127557
e_above_hull: 0.134595 eV/atom
Curie temperature: 745.58 K
No imaginary modes detected
Easy axis z: -7302.045922 eV (θ=0.0°, φ=0.0°)
Hard axis x: -7302.045903 eV (θ=90.0°, φ=0.0°)
ΔMAE (hard-easy): 0.018796 meV
Fe15Ir (space group: Pm-3m #221, crystal system: cubic, point group: m-3m)
Number of atoms in the cell: 16
Easy axis z: -35245.522685 eV (θ=0.0°, φ=0.0°)
Hard axis x: -35245.518820 eV (θ=90.0°, φ=0.0°)
ΔMAE (hard-easy): 3.865130 meV
Not a realistic candidate but an interesting test. Iridium is extremely expensive. More expensive than Platinum. But look at the size of that MAE 👀
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -28.5764 eV; energy change = -0.0556 eV; symmetry: Pmm2 → Pmm2
Number of atoms in the cell: 4
Easy axis x: -7645.989053 eV (θ=90.0°, φ=0.0°)
Hard axis z: -7645.989006 eV (θ=0.0°, φ=0.0°)
ΔMAE (hard-easy): 0.047192 meV
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -191.0519 eV; energy change = -0.0024 eV; symmetry: Imm2 → Imm2
Unable to test! Crashed the model. Not sure what's up at this point. It's a MatterGen generation - they've been giving me all sorts of trouble recently.
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -40.7885 eV; energy change = 0.0000 eV; symmetry: Pm-3m → Pm-3m
Number of atoms in the cell: 5
Easy axis z: -9726.391907 eV (θ=0.0°, φ=0.0°)
Hard axis x: -9726.391869 eV (θ=90.0°, φ=0.0°)
ΔMAE (hard-easy): 0.037788 meV
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -25.2515 eV; energy change = 0.0000 eV; symmetry: P6_3/mmc → P6_3/mmc
Number of atoms in the cell: 4
Magnetization density: 0.076451
e_above_hull: 0.184240 eV/atom
Curie temperature: 546.18 K
No imaginary modes detected
Easy axis x: -7960.833456 eV (θ=90.0°, φ=0.0°)
Hard axis z: -7960.830609 eV (θ=0.0°, φ=0.0°)
ΔMAE (hard-easy): 2.847346 meV
This was good to see! MnBi is a known good candidate. The first non-rare material with a high MAE I've seen. Struggles on Ms and Curie but it was still a good confirmation on the model's ability to predict.
Let's see if we can take what we found in MnBi and crank up the Ms a bit:
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -61.5567 eV; energy change = -0.0596 eV; symmetry: P4/mmm → P4/mmm
Number of atoms in the cell: 8
Magnetization density: 0.159473
e_above_hull: 0.254313 eV/atom
Curie temperature: 637.98 K
No imaginary modes detected
Easy axis y: -17840.774452 eV (θ=90.0°, φ=90.0°)
Hard axis z: -17840.771466 eV (θ=0.0°, φ=0.0°)
ΔMAE (hard-easy): 2.985789 meV
Exciting! Good MAE and good Ms from this one. Only issue is it's formation energy is high. ehull around 0.250.
Phase diagram of MnFe6Bi; e_above_hull: 0.254313 eV/atom; predicted_stable: False
Relaxed with Orb v3; 0.03 eV/Å threshold; final energy = -29.1047 eV; energy change = -0.0019 eV; symmetry: P4/mmm → P4/mmm
Number of atoms in the cell: 4
Magnetization density: 0.124042
e_above_hull: 0.01735 eV/atom
Curie temperature: 855.55 K
No imaginary modes detected
Easy axis z: -8851.951103 eV (θ=0.0°, φ=0.0°)
Hard axis x: -8851.947816 eV (θ=90.0°, φ=0.0°)
ΔMAE (hard-easy): 3.287396 meV
Pretty good performance. We need to figure out the role of Ni and if that is needed. All this MAE is coming from the Pt which is expensive, so we should figure out alternatives like MnBi.
Will be testing more throughout the day.